Y completed lap in 13 min and rest for 2. Both start walking together in same direction.How many minutes will it be until both meet again?
asked Jul 2, 2017

 Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: To avoid this verification in future, please log in or register.

Number of laps=n. It takes J 11n-1 minutes to do n laps; it takes Y 15n-2 minutes to do n laps.

In the time it takes Y to complete n laps, J has completed n+1 laps, so 11(n+1)-1=15n-2.

11n+11-1=15n-2; 12=4n so n=3. Therefore the time is 15*3-2=43 minutes (or 11*4-1=43 minutes).

The graph below shows that they meet up after 43 minutes, J having completed 4 laps while Y completes 3.

The more general solution is that J completes n+k laps while Y completes n laps:

11(n+k)-1=15n-2; 4n=11k+1; 4n=(8+3)k+1; n-2k=3k/4+1/4; m=(3k+1)/4 where m is an integer, and n=m+2k.

For m to be an integer the right-hand side must be divisible by 4, so k=4a+1 for integer a; so k=1, 5, 9, etc.

The lowest value for k is 1, so lowest value for m=1, and n=m+2k=1+2=3, making the shortest time 15*3-2=43 minutes.

answered Jul 2, 2017 by Top Rated User (582,840 points)